Looking at the math on Wikipedia: it appears that all space with changing surface gravity should emit it, but that objects much larger than their schwarzchild radius should emit much less radiation than the black hole they could make.

From what little I understand, when you move you get Hawking radiation from the event horizon induced by movement...

One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

eSOANEM wrote:idk, the usual arguments seem to require some sort of horizon (be it an event horizon or an unruh one) but then I've never actually seen a proper QFT in curved space derivation of it

That's the thing, the equations are for blackbody-matter holding it's coordinate position at a spatial location approaching (but not at) event horizon.

As for "proper QFT in curved space derivation of it": the explanation of the Unruh effect doesn't depend on curved space. As I understand it, there are necessarily two apparent horizons for a constantly accelerating particle, but those aren't directly related to unruh radiation. The "heat" comes from the blue-shifting of the vacuum.

wikipedia, Unruh_effect page wrote:The temperature of the vacuum, seen by an isolated observer accelerating at the Earth's gravitational acceleration of g = 9.81 m s−2, is only 4×10^−20 K

If an observer accelerating at g, experiences that temperature, then (by the equivalence principle) someone staying still on the surface of the earth should also experience it.

Looking at the math on Wikipedia: it appears that all space with changing surface gravity should emit it, but that objects much larger than their schwarzchild radius should emit much less radiation than the black hole they could make.

From what little I understand, when you move you get Hawking radiation from the event horizon induced by movement...

Can anyone help me with a hypothetical time dilation question? Just for funSo let's say in the case of the traveling twins they had an open line of communication between the rocket and earth. What if the twin in the rocket was playing "Glide" by Stone Temple Pilots which is exactly 5 minutes long? At what speed would the song play twice as fast as normal to the twin on earth? Five times as fast? I feel like there should be a handy chart for this issue that we will surely face some day in the future.

There are plenty of time dilation calculators online if you just google them, which you can use to get close to the correct result (didn't see one that goes by "enter time dilation factor > get velocity"). You can also just look at the formula for time dilation and solve for a ratio of 1/2 or 1/5 for the dilation factor. It's pretty simple algebra.

The factor is called λ (lambda) and is equal to (1-v²/c²)-½, where v is the speed and c is the speed of light in a vacuum. So for instance, if the moving twin has a speed of v = 4/5c = 0.8 c, then λ = 5/3 ≈ 1.67. In that case, the song which seems 5 minutes long to the twin on the rocket will seem λ · (5 minutes) = 25/3 minutes ≈ 8.33 minutes (8 minutes 20 seconds) long to the twin on Earth. On the other hand, if the relative speed is only v = 3/5c = 0.6 c, then λ = 5/4 = 1.25, and the song will only appear λ · (5 minutes) = 25/4 minutes = 6.25 minutes (6 minutes 15 seconds) long to the twin on Earth.

And remember there's also a Doppler shift depending on whether the traveling twin is moving toward or away from the stationary one.

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gmalivuk wrote:And remember there's also a Doppler shift depending on whether the traveling twin is moving toward or away from the stationary one.

Yes, as gmalivuk says, due to the doppler effect, the rate at which a transmitter moving relative to you will seem sped up (if it is moving towards you) or slowed down (if it is moving away from you) is not equal to the time dilation factor of the transmitter in your frame. To answer makeitstop's question, we have to use the relativistic doppler effect formula given here, in which the frequency of a signal you get from a transmitter is shifted by a factor of sqrt(1 + v/c)/sqrt(1 - v/c) relative to the frequency that would be measured by someone traveling along with the transmitter, where v is the velocity of the transmitter in your frame (positive if it's moving towards you, negative if moving away) and c is the speed of light. So if you want the frequency you measure to be twice the frequency seen by someone moving along with the transmitter, take the equation sqrt(1 + v/c)/sqrt(1 - v/c) = 2 and solve for v, which gives v = (3/5)c. So, a signal from a transmitter moving at 0.6c towards you would appear sped up by a factor of 2.

Without Doppler, there's no way to get the song to play twice as fast.

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Eebster the Great wrote:The important difference is that the observer on Earth knows there will be a Doppler shift and can correct for it. But there is no "correcting for" time dilation, because it is correct.

In what sense is the Doppler shifted rate less correct than the time dilated rate? After all, there is no frame-independent truth about the instantaneous rate one distant clock B is ticking relative to another clock A. It's true that in the type of coordinate system we call an "inertial frame", the time dilation equation gives the correct rate of B's ticking relative to coordinate time in the inertial frame where A is at rest. But you could also, if you liked, construct a non-inertial coordinate system where A is at rest, and where the Doppler shift equation would give the correct rate of B's ticking relative to coordinate time. If you're going to draw the line between "objective" or "physical" facts and facts which are more a matter of perspective, I think it makes the most intuitive sense to label as "objective" only those facts which are completely independent of the choice of coordinate system, like the proper time along a particular world between two events that lie along that worldline.

I think Eebster meant that the Doppler shift isn't a relativistic effect.

A stereo traveling toward you at half the speed of sound would seem to play twice as fast and at a higher pitch. We could easily correct for pitch. With a little patience, we could correct for playback rate.

If we tried to correct for time dilation with these effects, we'd make mistakes because the brothers genuinely experience different amount of proper time.

The thing about recursion problems is that they tend to contain other recursion problems.

Without Doppler, there's no way to get the song to play twice as fast.

Either you account for the Doppler shift, or you say there's no answer.

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Eebster the Great wrote:Or you make the song take twice as long instead of half as long.

Well sure, there are lots of ways you could answer different questions than the one that was asked.

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Assume instead of a song, the ship sends a ping at regular 1 second intervals. They'll be received, if i'm right, at longer intervals than that, eg. 2 second for v=0.866c.The thing is, the one on the ship will receive earth's pings at 2s intervals, also! As long as there's a relative movement, both will see the other as slowed down.

But what happens when the ship stops, and then reverses course? We know that the situation isn't symmetrical anymore, as both will agree that time on earth passed faster when the ship arrives back home.Do all the missing pings of earth pile up in the instant (disregarding de/acceleration times) of course reversal?

speising wrote:Assume instead of a song, the ship sends a ping at regular 1 second intervals. They'll be received, if i'm right, at longer intervals than that, eg. 2 second for v=0.866c.The thing is, the one on the ship will receive earth's pings at 2s intervals, also! As long as there's a relative movement, both will see the other as slowed down.

But what happens when the ship stops, and then reverses course? We know that the situation isn't symmetrical anymore, as both will agree that time on earth passed faster when the ship arrives back home.Do all the missing pings of earth pile up in the instant (disregarding de/acceleration times) of course reversal?

No, they come in at a greater speed during the whole trip back.

That's also a bit of a Doppler thing, though. If the shipboard twin calculates the time on Earth, according to the ship's reference frame, there will be a sudden jump when the direction reverses.

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Quizatzhaderac wrote:The relativistic Doppler effect and it's equation are just the straightforward combination of the concepts/equations of the Doppler effect and time dilation.

If you derive it in an inertial frame, sure. But all the terms of Doppler equation can be understood in terms of local measurements which don't depend on any particular choice of coordinate system (even the "v", which can be understood in terms of the change in delay for two successive light signals you send out to bounce back and return to you), which means you could derive the same equation using some non-inertial frame, including one which used a definition of simultaneity such that the two clocks remained synchronized as they moved apart (no time dilation).

Using quantum physics (specifically the phenomena of quantum entanglement), it is possible to send information faster than the speed of light. This is a direct contradiction to Einstein's Theory of Special Relativity. Einstien, Podolsky and Rosen were the first ones to point this out, so this problem is called the EPR Paradox. Their solution to this paradox was that there was stuff we do not know, which they named local hidden variables (LHV).

Although Bohr gave a response that this was not a paradox at all, more research is currently being done on Bell's response, which is called Bell's Theorem (a.k.a. Bell's Inequalities). I am not even going to pretend that I understand any of this in any way. The EPR Paradox and Bell's Theorem is so complex and has such important imprecation regarding the nature of The Universe, that the Stanford Encyclopedia of Philosophy has a article dedicated to each of these topics.*

jewish_scientist wrote:Using quantum physics (specifically the phenomena of quantum entanglement), it is possible to send information faster than the speed of light. This is a direct contradiction to Einstein's Theory of Special Relativity. Einstien, Podolsky and Rosen were the first ones to point this out, so this problem is called the EPR Paradox. Their solution to this paradox was that there was stuff we do not know, which they named local hidden variables (LHV).

This is basically the opposite. Quantum mechanics can most certainly not send information faster than the speed of light. EPR did not understand what it meant to send information when they proposed their initial work. There are correlations between spacelike separated observables, which require quantum mechanics to explain. Local Hidden Variables cannot explain the observed violations of Bell's Inequality (Bell's Inequality says that classical physics must give < a certain amount of correlation, and because it is exceeded, we require quantum mechanics.) But quantum mechanics is entirely local. All observables are defined locally, and all commutations are zero if the two observables are not casually connected (in a light cone.)

LE4dGOLEM: What's a Doug?Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

jewish_scientist wrote:Using quantum physics (specifically the phenomena of quantum entanglement), it is possible to send information faster than the speed of light. This is a direct contradiction to Einstein's Theory of Special Relativity. Einstien, Podolsky and Rosen were the first ones to point this out, so this problem is called the EPR Paradox. Their solution to this paradox was that there was stuff we do not know, which they named local hidden variables (LHV).

Although Bohr gave a response that this was not a paradox at all, more research is currently being done on Bell's response, which is called Bell's Theorem (a.k.a. Bell's Inequalities). I am not even going to pretend that I understand any of this in any way. The EPR Paradox and Bell's Theorem is so complex and has such important imprecation regarding the nature of The Universe, that the Stanford Encyclopedia of Philosophy has a article dedicated to each of these topics.*

Did you have, like, an actual question here, or just a summary of what some other people said?

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Okay, explain this to me, all you lay physicists (or, um, even any professional physicists, you're cool too):

Make a nice steaming mug of hot cocoa. Use a reasonably sturdy mug.

Put a spoon in the glass and begin steadily tapping at the bottom. The sound of the tapping will rise in pitch.

Do it less steadily. The pitch will not cease to rise. There will be no noticeable correlation between the rate or regularity of the tapping and the rate of change in pitch.

Walk away and leave the entire thing alone for a few minutes.

Come back and start tapping again. IT WILL CONTINUE AT THE SAME PITCH IT LEFT OFF AT.

Why is this? If the pitch rises due to, say, energy imparted to the glass or the beverage, it should decay over time, which would mean that a slower rate of tapping would result in a smaller rate of change in pitch, and walking away for a few minutes should cause the pitch to drop noticeably. If it's some kind of resonance in the chamber, it should simply emphasize frequencies close to the resonant frequency of the glass and de-emphasize others. The heck's going on here?

"'Legacy code' often differs from its suggested alternative by actually working and scaling." - Bjarne Stroustrupwww.commodorejohn.com - in case you were wondering, which you probably weren't.

I'm pretty sure it's not just a weird perceptual glitch, because A. I've repeatedly tested this and got the same results, and B. I've verified it with other people. Tried it with coffee (cream & sugar) and got the same result. Though I admit I've never recorded the audio and analyzed the pitch thusly.

"'Legacy code' often differs from its suggested alternative by actually working and scaling." - Bjarne Stroustrupwww.commodorejohn.com - in case you were wondering, which you probably weren't.

commodorejohn wrote:Though I admit I've never recorded the audio and analyzed the pitch thusly.

Yes, do science to it. And see if you can measure the temperature too (preferably of the cup and the liquid, firstly to see if there's any change of temperature, secondly to see if the change corresponds to a change in pitch).